Torus: Difference between revisions
(New page: ==Definition== A '''torus''' is a particular kind of Riemann surface. it is a Riemann surface obtained as the quotient of <math>\mathbb{C}</math> by a lattice. A torus is the same as...) |
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Latest revision as of 19:19, 18 May 2008
Definition
A torus is a particular kind of Riemann surface. it is a Riemann surface obtained as the quotient of by a lattice.
A torus is the same as an elliptic curve, though the latter description is typically used when we want to study it as an algebraic object. Topologically, a torus is a topological torus: a product of circles.
Not all tori are isomorphic as Riemann surfaces: in fact, two tori are isomorphic as Riemann surfaces iff the corresponding lattices are related by a scaling and rotation.